For improving the performance of optical frequency dissemination and the resolution of its out-of-loop (OOL) characterization, we investigate a compact free-space interferometer design in which a monolithic assembly forms the reference arm. Two interferometer designs are realized, and their environmental sensitivity is analyzed based on the properties of the materials involved. We elucidate that in these designs the temperature sensitivities of the out-of-loop signal paths are greater than for the reference arm. As the estimated temperature-variation-induced frequency transfer errors are observed to be the relevant limitation, the out-of-loop characterization signal can be regarded as a trustworthy upper limit of the frequency transfer error to a remote place. We demonstrate a fractional frequency transfer uncertainty and OOL characterization resolution of $\le 2.7\times {10}^{-21}$ over many measurement runs. With a value of $(0.23\pm 1.07)\times {10}^{-22}$ the weighted mean offset is significantly below the best reported results so far.